Math Digests May 2025

The maths that tells us when a scientific discovery is real – or not

New Scientist, May 8, 2025

In April, a team of physicists announce that they’d detected a molecule on a far-off planet that’s suggestive of life. They reported a 0.3% chance that their findings are an artifact of random noise in the data. That “might seem like pretty good odds – but in reality, it’s possible that the chance is actually close to zero,” writes Jacob Aron for New Scientist. Aron explains how scientists arrive at their confidence estimates, and why we might want to be skeptical even of statistically significant results.

Classroom Activities: probability, statistics, data

  • (Mid-level) To illustrate the idea of statistical significance, Aron uses the example of flipping a coin. We usually assume that coins are unbiased, meaning they have equal chances of landing on heads or tails. In pairs, play the following game to practice identifying a biased coin.
    • Each student gets a secret number between 0% and 100%. Half of all students will have an unbiased coin (50%); the other half will have a coin that could be biased in any direction, by any amount.
    • Put your secret number into this coin flip simulator, under “probability of getting tails.” Flip for 1 coin and 10 repetitions. Write down the resulting experimental statistics and show them to your partner. (Remember not to show your partner the theoretical statistics!)
    • Answer the following questions about your partner’s results:
      • What are the chances that you would get these results with an unbiased coin?
      • If the coin is biased, what is your best guess for your partner’s secret number?
      • Do you think the coin is biased? How confident are you in your answer?
    • Repeat the exercise for 100 and 1,000 coin flips.
    • (High level) After the game, reveal your secret numbers. Tally up how many students guessed right after each round of play. Are the results compatible with the confidence levels?
  • (High level) Read this blog post about statistical significance thresholds. Answer the following questions.
    • What is a p-value?
    • How is a p-value related to a “sigma”?
    • In the recent study about extraterrestrial life, the scientists reported 99.7% confidence. What does this mean?
    • How is “99.7% confidence” difference from “99.7% probability of a correct result”?

—Leila Sloman

When math meets medicine: How a mathematician turned grief into a mission

WUFT, May 7, 2025

Math gives scientists a language to describe chemical reactions and the spread of disease. Mathematician Helen Moore knows the impact of this all too well. WUFT’s Nicole Borman wrote about Moore’s experience losing a husband to cancer. That catastrophe propelled Moore to study math models that improve cancer drug regimens. “Math models simulate how cancer grows and responds to treatment, helping researchers test therapies faster and more safely,” Borman wrote.

Classroom Activities: pharmacokinetics, mathematical modeling

  • (High level) “Pharmacokinetics” is the study of how pharmaceutical compounds move throughout the body and change in concentration. This field commonly uses logarithmic functions of the form $y = A\log _{10}(x) + B$, and exponential decay functions of the form $y = Ce^{-kx}$.
    • Graph the logarithmic function for $y$, assuming $A = 1$ and $B = 1$.
    • On the same plot, graph the exponential decay, assuming $C = 1$ and $k = 0.25$.
    • Explain the difference in how each function changes with $x$.
    • If the variable $x$ represents time, give one example for each function of what $y$ could represent. Describe what each plot illustrates in your examples. (Hint: these functions can also be used to model the growth or decay of wealth.)
  • For more explanation, watch the videos in the How Math Fights Cancer graphic of the article.

—Max Levy

Is every bag of Skittles unique? An Oxford mathematician calculated the rainbow, and these 15 reactions were sweet

The Poke, May 30, 2025

“No two rainbows are the same. Neither are two packs of Skittles.” At least, that’s what Mars, Inc. wants you to think. In a TikTok video posted by the Oxford Department of Mathematics, admissions coordinator James Munro investigates the claim. “I’ve done a lot of counting,” Munro says. The results? He estimates 3 million unique bags of Skittles, compared to 185 million bags sold in 2017. Satire outlet The Poke covers the video, joking: “We can all sleep at night now.”

Classroom Activities: counting, partitions

  • (All levels) Watch the TikTok video, and then answer the following questions.
    • James Munro is testing the mathematical claim “no two packs of Skittles are the same.” What does it mean for two packs of Skittles to be the same, according to Munro?
    • What quantity did Munro calculate? Why do his calculations mean the claim is false?
    • Is there another way to interpret the claim “no two packs of Skittles are the same”?
  • (Mid-level) Now, we’ll try to recreate Munro’s calculation in a simpler world where there are only 2 colors of Skittles: red and green. We will consider two packs of Skittles “the same” if they have the same number of red candies and the same number of green candies. (Does this match your answer above?)
    • If each pack of Skittles has 5 candies total, how many different possible packs are there?
    • Come up with a formula that tells you how many packs with N total candies there are, for any number N.
    • Munro says that Skittles can come in packs as small as 30, or as big as 50. If N can be anything between 30 and 50, how many possible packs are there?
    • Repeat these calculations for a world where Skittles come in three colors, instead of just two.
    • (High level) Find a recursive formula to calculate the number of packs with C colors and N total candies.
  • (High level) TikTok commenter Matthew Hannaway responded: “The chance of getting all reds in a bag of 30 is 1 in 538 quintillion. (That is a genuine calculation), So there are certainly more than 3 million possibilities.” Is Hannaway’s calculation correct? Is his conclusion correct? Why or why not?

—Leila Sloman

Meet one of the ‘world’s most interesting’ mathematicians

Science News Explores, May 9, 2025

Angela Tabiri recently earned the title of “world’s most interesting mathematician” in an internet competition. The competition was all about explaining math concepts in a relatable way. “Windows in a house, for instance, can show why angles and geometry are important,” wrote Lakshmi Chandrasekaran for Science News Explores. Tabiri won with a mix of demonstrations from dance to crafts. She recently spoke with Science News Explores about how she became a mathematician and how she inspires students to follow in her footsteps.

Classroom Activities: geometry, pi, storytelling

  • (All levels) Using flash cards, test yourselves on the Power Words at the bottom of the article in small groups.
  • (All levels) Using the explanation in the article’s introduction, measure the circumference and diameter of four circular objects in your classroom.
    • Tabulate the measurements.
    • Calculate the ratio of each circumference to each diameter.
    • Explain how and why this calculation compares to $\pi$.
  • (High level) Tabiri describes the power of stories to explain technical concepts. In small groups, assign one of the following geometry concepts to each group member. Come up with a brief story that explains each concept. (As an example, see the Game of Rice story about how quickly numbers grow when doubled.)
    • Symmetry
    • The length of a hypotenuse
    • The three types of triangles
    • The difference between congruence and similarity
    • The difference between translation, rotation, and reflection

—Max Levy

How Can AI ID a Cat? An Illustrated Guide

Quanta Magazine, April 30, 2025

This article from Quanta Magazine explains how machine learning algorithms can identify cats in images. “That’s not because a clever programmer discovered a way to isolate the essence of ‘catness’,” wrote Ben Brubaker. Brubaker and illustrator Mark Belan present simple examples of the systems that learn to categorize images, which are called neural networks. They explain how computer vision relies on mathematics in (many) more than three dimensions.

Classroom Activities: artificial intelligence, higher dimensions

  • (Mid-level) Read the article and then answer the following questions in your own words.
    • What is a classification task?
    • What is a neural network?
    • How does a neural network identify cats without seeing the “catness” that you might see?
  • (Mid-level) Imagine your neural network classifies points as being either red or blue, and its initial guess for the classifier equation is the line $y=x$. Plot this equation for $x$-values from 0 to 1 and $y$ from 0 to 1.
    • If every point in the region above the line is considered “red” and every point below the line is considered “blue,” to what region does the point $(0.4,0.8)$ belong?
    • If the point $(0.5,0.3)$ is actually red, does our $y=x$ equation accurately classify it?
    • What is one way in which the equation can change to correctly classify the point?
    • Describe this change mathematically and in terms of “weights” or “bias.”
    • (High-level) Assume that the point $(0.4,0.8)$ and $(0.5,0.3)$ are still red. If the points $(0.1,0.8)$ and $(0.9,0.4)$ are both actually blue, can the classifier still be a line? If not, how must the equation and neural network change?
  • (High level) How many mathematical dimensions are required to detect cats in 50 pixel by 50 pixel black and white images?
    • What does each dimension represent?

—Max Levy

More of this month’s math headlines